This article is cited in 10 papers

The intermediate Jacobian of the double covering of $P^3$ branched at a quartic

A. S. Tikhomirov


Abstract: In this paper we study the intermediate Jacobian $J_3(X)$ of a double covering $X$ of $P^3$ branched at a smooth quartic which does not contain projective lines. We prove an analogue of the Riemann theorem for the Poincare's divisor of the intermediate Jacobian $J_3(X)$, the global Torelli theorem for $X$, and the nonrationality of $X$.
Bibliography: 13 titles.

UDC: 512.776

MSC: Primary 14E20, 14J30, 14K30; Secondary 14J15, 14J25, 14C30, 14E22, 14E35, 14M20, 14N05, 3

Received: 23.04.1980

 English version: Mathematics of the USSR-Izvestiya, 1981, 17:3, 523–566

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